Effective electroweak Hamiltonian in the gradient-flow formalism

Abstract

The effective electroweak Hamiltonian in the gradient-flow formalism is constructed for the current-current operators through next-to-next-to-leading order QCD. The results are presented for two common choices of the operator basis. This paves the way for a consistent matching of perturbatively evaluated Wilson coefficients and non-perturbative matrix elements evaluated by lattice simulations.

arXiv comment6 pages, 1 figure, 1 ancillary file. v2: minor clarifications, matches published version

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• One-loop matching of the $CP$-odd three-gluon operator to the gradient flow
• Short-flow-time expansion of quark bilinears through next-to-next-to-leading order QCD
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• Stout smearing and Wilson flow in lattice perturbation theory
• Two-loop gradient-flow renormalization of scalar QCD
• The gradient flow formulation of the electroweak Hamiltonian
• One-loop matching of the LEFT to the QCD gradient flow
• Gradient-flowed order parameter for spontaneous gauge symmetry breaking